This invention relates to a method of creating the curved surface of a three-dimensional body and, more particularly, to a method of creating curved surfaces that is ideal for the preparation of a numerical control tape required for the numerically controlled machining of a three-dimensional metal mold or the like.
A curved surface of a three-dimensional metal mold or the like, when drawn out on the plane of a blueprint, is generally represented by a plurality of given section curves, but no data is shown for the shape of the area lying between a certain section curve and the next adjacent section curve. When carrying out numerically controlled machining it is essential that these two section curves be connected smoothly despite the fact that the shape of the area between them is not given. In other words, this means that machining must be performed by generating the curved surface between the two section curves from such data as that indicative of the section curves, punching an NC tape so as to incorporate the data concerning the generated curved surface, and then machining the workpiece in accordance with the instructions on the NC tape. To this end, the numerical control tape ordinarily is prepared by using a computer, and either of two methods can be adopted to create the curved surface, namely (1) a patch system in which processing is executed by partitioning a curved surface into minute portions, and (2) a system in which a two-dimensional curve made of straight line segments and arcs is modified for each pick-feed applied to a third axis.
The patch system (1), however, entails the processing of large quantities of data as well as highly complicated mathematical processing, and requires a large-scale computer system. The system (2) makes processing with a small-scale computer possible, but there is no three-dimensional tool offset capability and an excessive limitation upon tool movement direction and machining shape, making it impossible to create sophisticated three-dimensional bodies.
Accordingly, the inventors have already proposed a method of creating curved surfaces, comprising generating a plurality a intermediate sections and finding a section curve (intermediate section curve) on a curved body, based on the intermediate sections, in accordance with predetermined rules, from section data specifying given sections of a three-dimensional curved body and from data specifying section curves in said sections, and generating the curved surface of the three-dimensional body based on the plurality of generated intermediate section curves. In accordance with such a method, processing can be carried out with a small-scale computer and a sophisticated three-dimensional body can be created in a simple manner.
Heretofore, a three-dimensional curved body has been generated by partitioning the X, Y or Z axis in accordance with a partitioning quantity provided for the X, Y or Z axis irrespective of the position, shape, etc. of the curved surface, generating intermediate sections so as to contain partitioning points obtained from the partitioning operation, finding a section curve (intermediate section curve) in each of the intermediate sections, and generating the three-dimensional curved body on the basis of a plurality of the intermediate section curves. Machining has been performed by transporting a tool along the X, Y or Z axis through a cutting pitch decided in accordance with the partitioning quantity (which operation is referred to as a pick-feed operation), then transporting the tool along an intermediate section curve, followed by repeating the pick-feed operation and the tool movement along an intermediate section curve, whereby the desired three-dimensional curved body is created.
FIG. 1(a) shows an example of the conventional method, including steps of partitioning the Z axis in accordance with a given partitioning quantity, generating a plurality of intermediate sections Si (i=1,2 . . . n) so as to contain partitioning points di (i=1,2 . . . n), finding section curves Ci (i=1,2, . . . n) in the intermediate sections, and performing machining by moving a tool TL along the section curves. FIG. 1(b) shows another example of the conventional method, including steps of partitioning the X axis in accordance with a given partitioning quantity, generating a plurality of intermediate sections Si (i=1,2 . . . n) so as to contain partitioning points di (i=1,2 . . . n), obtaining section curves Ci (i=1,2, . . . n) in the intermediate sections, and performing machining by moving a tool TL along the section curves.
Thus, with the prior-art method, the partitioning pitch quantity can be given without being hampered by the position or shape of the curved surface. However, the conventional method does have the following defects:
(1) When instructing the axis along which the partitioning pitch is to be taken, it is difficult to judge whether the desired curved body of an acceptably small machining error will be obtained. For example, it is general practice to provide for a partitioning quantity along the Z axis [FIG. 1(a)]. However, in a case where the curved surface has a gentle incline along the X axis [FIG. 1(b)], providing the partitioning quantity along the X axis makes it possible to obtain a greater number of partitions so that the curved surface can be generated and machined more accurately.
Accordingly, in a case where the curved surface of the curved body CB of the type shown in FIG. 2(a) is to be generated, it is difficult to judge along which axis the partitioning pitch should be given. [See FIGS. 2(b), (c) and (d).]
(2) Depending upon the shape of the curved surface, the curved surface is partitioned and a desired partitioning axis of desired partitioning pitch must be given for each surface. For example, as shown in FIGS. 3(a) and (b), there are cases where the curvature of the section curve SC of the curved body CB differs depending upon location [at portions (A) and (B)]. In order to obtain a curved surface of uniform smoothness in such cases, the axis along which partitioning is to be performed for the portions (A) and (B) must be changed. As a result, NC data must be created by partitioning the curved surface and generating a curved surface for each surface. This complicates the creation of the curved surface. FIGS. 4(a) and (b) show the machined shape of the curved surface depicted in FIG. 3(a) in a case where the partitioning axis is changed from the Z to the X axis [FIG. 4(a)], and in a case where no change is made [FIG. 4(b)]. When there is no change in the partitioning axis [FIG. 4(b)], machining accuracy declines owing to an increase in unmachined sections at portion (A), as indicated by the shaded portion. On the other hand, when the partitioning axis is changed, the unmachined sections are greatly reduced, thereby enhancing machining accuracy over the foregoing case, as illustrated in FIG. 4(a).
It will be seen, therefore, that in a case where the curvature of a curved surface undergoes a major change, machining accuracy cannot be improved unless the partitioning axis is changed in accordance with the change in curvature. When the partitioning axis is changed, however, processing for the creation of the curved surface becomes more complicated.
Accordingly, an object of the present invention is to provide a curved surface creation method which enables a curved surface to be created and machining accuracy improved without changing the partitioning axis, even in a case where the curvature of the curved surfaces changes.